Overview

The course provides an introduction to the differential geometry of curves and surfaces, including the relevant notions of curvature, with an emphasis on global theory. Students will develop a deep understanding of the differential geometry of curves and surfaces, including the various relevant notions of curvature. This will require a synthesis of geometric visualization, symbolic and numerical calculation, and rigorous reasoning and communication. At the end of the course, students should be prepared for a graduate course in the differential geometry of manifolds.

The following books may be useful additional resources:

Differential Geometry of Curves and Surfaces, by Manfredo P. Do Carmo

Elementary Differential Geometry, by Barrett O’Neill

Elementary Differential Geometry, by Andrew Pressley

Differential Geometry of Curves and Surfaces, by Thomas Banchoff and Stephen Lovett